Why are there all these centralized mining pool operations up in my decentralized currency? Shouldn't there be a sister blockchain for mining share verification to which the bitcoin software could refer in automatically divvying up new coins? Miners would have plenty of incentive toward giving equal time to it in order to keep each other honest.

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It's irrelevant because of the implications of all the mining pools being voluntary.

So, the worries I've read on this forum about a single pool becoming larger than 50% of the network and giving its members or administrator the power to double-spend are completely unfounded?

They could only do it once. And it would be detected the next time a miner not in that 50% majority found a block. To be practical, it would have to be MUCH more than 50%, maybe closer to 70% or even 90%.

So, the worries I've read on this forum about a single pool becoming larger than 50% of the network and giving its members or administrator the power to double-spend are completely unfounded?

They could only do it once. And it would be detected the next time a miner not in that 50% majority found a block. To be practical, it would have to be MUCH more than 50%, maybe closer to 70% or even 90%.

So, the worries I've read on this forum about a single pool becoming larger than 50% of the network and giving its members or administrator the power to double-spend are completely unfounded?

No, not completely. However, so far the bitcoin economy has proven very good at self-regulation. An example: Deepbit did reach the > 50% mark recently; in response, a lot of people left the pool and joined other ones. I don't doubt that this level of corporate responsibility is due to the quality of our community. At the risk of sounding pompous, I think most of us here are of above average intelligence. I have good reason to think so: most of the discourse here is pretty well-informed, and most early adopters tend to be of the aforementioned set anyway. Highly intelligent people tend to enjoy new ideas and are more likely to adopt them.

Eventually bitcoin will go mainstream and with it will come the risk of monopoly as less conscientious users begin to pour in. But as long as the majority of miners remain both intelligent and socially conscientious, we should be good.

Though creating a decentralized mining pool would be awesome and a really, really effective long term solution to this potential problem. I'd be happy to see such a project come to fruition. :-)